Both goalkeepers were excellent, particularly Liverpool's Simon Mignolet, Joe Allen missed a sitter for the visitors, Everton's Kevin Mirallas netted and was then lucky to escape a red card for a wild lunge on Luis Suarez, who also scored, and there were 30 shots in the game, 17 on target.
Even in the four minutes of stoppage time there were more chances than in many a goalless draw and when the final whistle went nobody seemed quite sure whether to be delighted or disappointed.
Romelu Lukaku grabbed two Everton goals, including a classic header in the 82nd minute that lifted the home crowd off their feet as they thought they were about to see their side come from behind to win a league derby for only the second time in 90 years.
It was not to be but the Belgium striker on loan from Chelsea was still beaming after the match.
"That is the best experience I've ever had in club football," said Lukaku.
Pundit and former Liverpool defender Alan Hansen was also effusive in his praise.
"I played in over 30 of these but I don't think I've ever seen anything like this," he told BBC radio.
"It's 3-3 and both goalkeepers played brilliantly. It could have been 7-7 and even in stoppage time both teams were still really going for it.
"From the first minute it was absolutely magnificent to watch and I've never seen an Everton v Liverpool game so open, even the 4-4 game in 1991. This was terrific, just brilliant to watch, and I don't think either team deserved to lose."
DALGLISH RESIGNATION
That 4-4 FA Cup replay draw in 1991, that led to the resignation of Kenny Dalglish as Liverpool manager, is widely considered the best derby of the modern era although the FA Cup finals of 1986 and 1989 and the semi-finals of 1971 and 1977 are also remembered fondly - by Liverpool fans at least.
Everton's derby record in recent years has been poor, with just one win in 14 league meetings, but they took pleasure last season as they finished above their neighbours for the second successive top flight campaign for the first time since 1937.
Saturday's game was Everton manager Roberto Martinez's first taste of the always-frantic occasion, after he replaced David Moyes at the start of the season.
"We were magnificent in terms of the amount of chances we created. Simon Mignolet was man of the match and rightly so," said Martinez whose wife gave birth to a baby girl on Thursday.
"We are really disappointed to concede three goals from dead-ball situations but to be able to get the third goal was down to an outstanding performance from my players."
Brendan Rodgers was the happier of the two former Swansea City managers going head-to-head and felt able to appreciate the wider appeal of the match even though he missed out on a win that would have taken Liverpool top of the league for a few hours.
"It was a terrific game. I've been involved in a few (derbies) and they are real heart-stoppers," he said.
"We again showed our resilience and ability to fight back. This is a difficult place to come and they haven't lost at Goodison Park this year. All-in-all a wonderful game."
Rodgers complained that Mirallas should have been sent off for his reckless lunge on Suarez while Martinez countered with a claim that Steven Gerrard was lucky to escape punishment for elbowing Gareth Barry.
All grist to the mill on derby day and even if the teams had to settle for a draw, the Premier League, its ever-growing worldwide army of fans, and BT Sport who paid millions for the TV rights and showed the match, will all feel like winners.
(Editing by Tony Jimenez)
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